Slipping mechanics during walking along curved paths depend on the biomechanical context at slip onset

Curvilinear walking is common, causing limb- and radius-dependent asymmetries that distinguish it from straight walking and elevated friction demands that increase slip-and-fall risk. However, it is unclear how aspects of curvilinear walking influence the slip perturbations experienced. We cross-sectionally examined how three biomechanical slip contexts (slip onset phase, slipped foot relative to the path, path radius) influence slip direction, distance, and peak velocity. Eighteen young adults experienced unconstrained inside or outside foot slips during early, mid-, or late stance while following 1.0- or 2.0-m radius semicircular paths. We derived slip mechanics from motion-capture data and assessed their dependence on slip context using mixed-effects models. As slip onset phase progressed, slip directions exhibited an anterior-to-posterior transition, shortened mediolaterally, and accelerated anteroposteriorly. The slipped foot modified the direction transition, with inside and outside foot slips moving contralaterally and ipsilaterally, respectively. Inside foot slips were shorter and slower mediolaterally and longer anteroposteriorly than outside foot slips. Increasing path radius caused slips with greater mediolateral direction components. We show a range of context-dependent slips are possible, likely due to instantaneous magnitudes and orientations of shear ground reaction forces. Our results contribute to a comprehensive understanding of walking slips, which fall prevention methods can leverage.


Tuning the Circular Mixed Effect Model
The circular mixed effects model was created using the R package "bpnreg", which uses an embedding method to generate bivariate estimates of each coefficient in the model equivalent to x-and y-coordinates on the unit circle 1-5 . Because model coefficients are estimated using a Markov Chain Monte Carlo sampler, the number of model iterations, burn-in period (i.e. the first n iterations to exclude from the final estimate calculation to only include samples that have converged), and lag (i.e. every n th sample is included in each estimate calculation to prevent autocorrelation between samples) must be determined to ensure all coefficients converge on reliable estimates. To tune the model parameters, five iterations of the circular mixed effects model were run in parallel to generate five different sets of posterior estimates. The outcomes of these five models were then evaluated for convergence by calculating the potential scale reduction factor for each coefficient estimate. Factors near or equal to 1 indicate that additional iterations of the model will not improve convergence and, therefore, that the parameters are sufficient to generate reliable coefficient estimates [6][7][8] . Multivariate potential scale reduction factors (MPSRF) for the first and second components of each coefficient estimate are presented here to summarize the convergence Supplementary Figure S1: Gelman plots of the potential scale reduction factor for the first component of each coefficient estimate in the model up to 10,000 model iterations and the MPSRF for the first component at 10,000 iterations, a burn-in period of 2,000 iterations, and lag of 3.

Intercept
Mid

Component I Gelman Plots
results of the parameters entered into the final model in our analysis. To further assess convergence, Gelman plots were generated for both components of each coefficient estimate (Supplementary Figs. S1 and S2) 8 .
After iteratively adjusting the parameters entered into the five parallel models, we settled on 10,000 iterations, a burn-in period of 2,000 iterations, and a lag of 3 for our final circular model used in the analysis. We also entered a seed value of 101 to ensure the final model returned the same results after every execution. The choice of 101 is arbitrary, it only fixes the "starting point" of the model. No seed was entered when tuning the model. Trace

Transforming Bivariate Coefficient Estimates
The bivariate coefficient estimates output by the circular mixed effects model are difficult to interpret in terms of direction. Univariate estimates of direction can be derived from the bivariate output of the model since component I and II of each coefficient estimate is analogous to an x-and y-coordinate, respectively. The function "coef_circ" contained within the "bpnreg" R package performs this conversion on all outcome measures of the model 2 using the two-argument arctangent (atan2) function. The atan2 function works as follows 3 : The atan2 function returns univariate estimates of direction in a range of -180°-180°. Because we present our results in a range of 0°-360°, negative direction values were further converted to their positive counterparts by adding 360° to the negative value. Describe any efforts to address potential sources of bias Study Size 10 Explain how the study size was arrived at Quantitative Variables 11 Explain how quantitative variables were handled in the analyses. If applicable, describe which groupings were chosen and why a) Describe all statistical methods, including those used to control for confounding b) Describe any methods used to examine subgroups and interactions c) Explain how missing data were addressed d) If applicable, describe analytical methods taking account of sampling strategy e) Describe any sensitivity analyses